Our method for classifying nilpotent Zinbiel algebras is based on the calculation of central extensions of nilpotent algebras of smaller dimensions from the same variety.
The algebraic study of central extensions of algebras has been an important topic for years [1]}, [2]}, [3]}.
First, Skjelbred and Sund used central extensions of Lie algebras to obtain a classification of nilpotent Lie algebras [3]}.
Note that the Skjelbred-Sund method of central extensions is an important tool in the classification of nilpotent algebras.
Using the same method,
small dimensional nilpotent
(associative,
terminal [5]}, Jordan,
Lie [6]}, [7]},
anticommutative algebras,
and some others) have been described. Our main results related to the algebraic classification of cited varieties are summarized below.
